•34. A planning board in Elm County is interested inestimating the proportion of
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•34. A planning board in Elm County is interested inestimating the proportion of its residents that are in favor ofoffering incentives to high-tech industries to build plants in thatcounty. A random sample of Elm County residents was selected. Allof the selected residents were asked, “ Are you in favor ofoffering incentives to high-tech industries to build plants in yourcounty?” A 95 percent confidence interval for the proportionof residents in favor of offering incentives was calculated to be0.54 ± 0.05. Which of the following statements iscorrect? •(A) At the 95% confidence level, the estimate of 0.54is within 0.05 of the true proportion of county residents in favorof offering incentives to high-tech industries to build plantsin the country. •(B) At the 95% confidence level, the majority of areasresidents are in favor of offering incentives to high-techindustries to build plants in the county. •(C) In repeated sampling, 95% of sample proportionswill fall in the interval (0.49, 0.59). •(D) In repeated sampling, the true proportion of countyresidents in favor of offering incentives to high-tech industriesto build plants in the county will fall in the interval (0.49,0.59). •(E) In repeated sampling, 95% of the time the trueproportion of county residents in favor of offering incentives tohigh-tech industries to build plants in the county will be equal to0.54. •34. A planning board in Elm County is interested inestimating the proportion of its residents that are in favor ofoffering incentives to high-tech industries to build plants in thatcounty. A random sample of Elm County residents was selected. Allof the selected residents were asked, “ Are you in favor ofoffering incentives to high-tech industries to build plants in yourcounty?” A 95 percent confidence interval for the proportionof residents in favor of offering incentives was calculated to be0.54 ± 0.05. Which of the following statements iscorrect? •(A) At the 95% confidence level, the estimate of 0.54is within 0.05 of the true proportion of county residents in favorof offering incentives to high-tech industries to build plantsin the country. •(B) At the 95% confidence level, the majority of areasresidents are in favor of offering incentives to high-techindustries to build plants in the county. •(C) In repeated sampling, 95% of sample proportionswill fall in the interval (0.49, 0.59). •(D) In repeated sampling, the true proportion of countyresidents in favor of offering incentives to high-tech industriesto build plants in the county will fall in the interval (0.49,0.59). •(E) In repeated sampling, 95% of the time the trueproportion of county residents in favor of offering incentives tohigh-tech industries to build plants in the county will be equal to0.54.Explanation / Answer
The anwer is D); a confidence interval is the range of values in which the true proportion (or mean, for that matter) falls in the interval the percentage of time indicated by the level of confidence (i.e. In repeated sampling, 95% of the confidence intervals will contain the true proportion.)
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